3. Problem 3 The equation Ax2 + y + 2z = 4 (where ) is a constant) defines a quadric surface when graphed in R3, but the exact nature of this shape depends on the value of 1. (a) (Evaluated for justification and written explanation) If A = 0, this shape is a (parabolic) cylinder. Explain what a "parabolic cylinder" is, and why the equation y2 + 2z = 4 is the graph of one. Explanation: (Use complete sentences) (b) (Evaluated for justification and written explanation) If > # 0, this shape is either a hyperbolic paraboloid, or an elliptic paraboloid. Explain the difference between these two shapes, which values of A correspond to which shape, and how the traces of each shape are influenced by the choice of 1. Explanation: (Use complete sentences)